I actually doubt most slaves in say, the Roman Empire era and earlier had the sort of opinion that “slavery as an institution is evil.” Back then slavery was seen as a sort of temporary state that you were brought to mostly due to bad fortune or sometimes bad decisions (for example becoming so indebted.)
While Rome wasn’t a society with great social mobility, there are many stories of slaves becoming slave owners.
Slavery actually was widespread and common throughout many parts of Europe up until the year 1500 AD. Where it went away it was replaced with serfdom, which to a modern observer was very little different from slavery itself. In fact, serfdom as it was practiced in Russia was the same in every respect as slavery outright (Russian serfs could be relocated at will, were frequently moved from being farmers to industrial workers, Russian boyars and seigneurs frequently had serf harems and even sent some of their serfs off to academies to learn the performing arts so the great Russian landed aristocracy could have their own personal serf theaters.)
I’d say at least up until the point in history where we can say a “significant” portion of the population recognized serfdom as being morally wrong, we can’t really say that most people recognized slavery as being wrong. By and large the move from outright slavery to serfdom (which again, in many ways was little different than true slavery) was one of economic self-interest for the nobility and not a move of political enlightenment.
Emperor Joseph at the end of the 18th century started to indicate that he believed serfdom to be a moral wrong, but even as Emperor he was unable to abolish it. (I believe it persisted in the Habsburg Empire until 1848.)
By and large in continental Europe, I’d say most people, from serf to King were taught that it was for the good of all that there was a small class of people who ruled and owned mostly everything and a large bulk of people who were bound permanently to service to the ruling class. Obeying and supporting that system was taught as the religious and Christian behavior, so in fact trying to advocate against said system was viewed as a sin.
Interestingly, in most of the places in Europe where serfdom died earliest (it was considered an obsolete practice by the 15th-16th century in England), it went out of practice because it was viewed as being economically inefficient compared to other ways of organizing and running agricultural communities. [As a total aside, slavery as practiced in America prior to the American Civil War was not at all in the economic interests of anyone, even the large plantation holders would have done better under a different system if they had the education and intelligence to run things better.]
Ultimately, the question is “when should a reasonable person have known slavery was evil?” Well, I’d say prior to 1700 in Europe, “reasonable” persons would be hard to find. Most people prior to 1700 in Europe were illiterate, believed anything they were told, and did not question authority. I’d say prior to 1700 the only people that might think slavery evil (and I consider serfdom to essentially be a form of slavery) were a few enlightened, educated members of the nobility or the clergy. Even in the European countries that had more or less abandoned the seigneurial system prior to 1700, in those cases it was a change for economic improvement and not a morality thing.
Probably the earliest country in which an average person plucked out of a local tavern would know slavery was immoral would be in England, possibly as early as the 1600s, but even then I suspect most Englishmen would not view the enslavement of non-Christians as immoral. Keep in mind it was for many years that in England it was considered moral to persecute Catholics and even kill them.
Now, all that being said the 1700s were momentous for two reasons. Firstly, there was a communication revolution (I won’t get into it, but realize that before the modern era a country like France was more a patch work of regions that most people were born and died in, never leaving the area around their small village), due to better roads and national level governments that began to understand the importance of a maintained road system. Secondly, the overall increase in wealth lead to more people who could read (it was obviously still common to be illiterate) and thus more people who started to have informed ideas about things and greater moral issues. By the end of the 1700s if you couldn’t read you still probably were exposed to the news because many taverns and other meeting places had several people in them who would read the news to their illiterate friends.
The increase and exposure of the masses to the written word, and the increase in communications meant there was finally enough underlying structure for genuine moral ideas to actually spread and be considered by a wide portion of the population. (Much of European history omits the fact that the lion’s share of the people were kept ignorant, bound to a master, and poor. Most of the great thought and achievements that came before the 18th century in Europe only happened within the small portion of human society that was lucky enough to be born into the ruling class.) So I can say with some confidence that by the end of the 18th century most people probably should have known or at least considered the possibility that slavery was evil.
Certainly Americans of 1850, to a man, should have been able to conclude this from all that they knew of the world.